Question

What is the solution of 16^(-3n+2)=64

Answer 1

Hint: 4^3=64, and hence 16^(3/2)=64

Answer 2

Now I'm even more confused...

Answer 3

hint: \(\bf 16^{-3n+2}=64\qquad
\begin{cases}
64=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\to 2^6\\
16=2\cdot 2\cdot 2\cdot 2\to 2^4
\end{cases}
\\ \quad \\
16^{-3n+2}=64\implies (2^4)^{-3n+2}=(2^6)\)

Answer 4

So you would need to get similar bases then solve? That's so much easier than what I was thinking of

Answer 5

well... yes

thus \(\bf 16^{-3n+2}=64\implies (2^4)^{-3n+2}=(2^6)
\\ \quad \\
2^{2(-3n+2)}=2^6\implies 2(-3n+2)=6\)

Answer 6

And that's what I got when I solved, n=6. Thanks!

Answer 7

hmmm

Answer 8

@jdoe0001 Could you help me with another problem?

Answer 9

\(\bf 2^{2(-3n+2)}=2^6\implies 2(-3n+2)=6\implies -6n+4=6\)

don't forget to distribute

Answer 10

or you could divide by 2 first either way, is not 6

Answer 11

but you can always post anew for another one, sure
more eyes, and if I dunno, someone else may know :)

Answer 12

Are you sure the answer isn't 6?

Answer 13

well.. let's check it
let us set n = 6

so we know that 2(-3n+2) =6

so n = 6 thus
2( -3(6) +2 ) =6
(-3(6) + 2) = 3
-18 + 2 = 3
-16 \(\ne\) 3

Answer 14

Refer to the solution calculation using the Mathematica 9 program.